Goals from Kari Arnason, Youl Mawene and Andrew Considine gave the Dons back-to-back wins for the first time in the Clydesdale Bank Premier League this season.
Brown's side had received plenty of criticism after failing to score in seven of their opening nine SPL matches but this win coupled with their 4-0 thrashing of Dunfermline means they have now hit the back of the net seven times in two games.
The Aberdeen manager said: "It possibly wasn't as resounding as the last home game against Dunfermline but I think it was a very competent performance against Dundee United who are one of the better sides in the SPL in my opinion.
"To be three up after an hour was very good going and I think we deserved to be because we played well. We are obviously still trying to improve but the last two results have vindicated my contention that we are a better team than the results we have achieved and the league position indicated. We are not as bad as people were making us out to be."
The win sees the Dons leapfrog the Terrors to move up to seventh in the league ahead of an Old Firm double-header.
Brown added: "The confidence is returning but we were always a confident enough team. We didn't get any breaks at all in the first half-dozen games in the league and now we are getting a break or two. I think you can see we will be a difficult team to beat as well so I'm optimistic about the remainder of the season.
"However we are not getting carried away because we have won a couple of games and we are desperately disappointed we conceded that goal at the end.
"It's maybe being a bit greedy but I felt there was a bit of an anti-climax to the result in the end. If you said to me we would win 3-1 against a very good Dundee United I would have said thank you very much."
United manager Peter Houston admitted his side need to improve defensively after having conceded nine goals in three matches.
He said: "When you look at the goals we lost today I felt that the Aberdeen players showed more desire to get their head on the ball. If we are going to ship goals from set-plays then we have a major problem. There is no doubt that we aren't defending properly.
"That is something we will have to have a look at and work hard on. It was a disappointing second half performance and there is no point lifting the ante when you are already 3-0 down."
Source: Team Talk